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The Effect of Vacuum Fluctuations on Quantum Metrology for a Uniformly Accelerated Atom

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Abstract

We studied, in the framework of open quantum systems, the dynamics of the quantum Fisher information of the parameters of the initial atomic state and atomic transition frequency for a uniformly accelerated polarizable two-level atom coupled in the multipolar scheme to a bath of fluctuating vacuum electromagnetic fields in Minkowski space-time. Our results show that the vacuum fluctuations in Minkowski space-time always make the quantum Fisher information decay, thus degrade the precision of the parameter estimation. The acceleration of the atom makes the quantum Fisher information of initial parameters of atomic state decay faster than those in case with static atom in Minkowski vacuum and even those in case with static atom in Minkowski thermal bath with corresponding Unruh temperature. The maxima of quantum Fisher information of atomic frequency and the optimal measurement time are shown to be smaller than those in the static atom in vacuum case as well as those in the corresponding thermal case.

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References

  1. Helstrom, C.W.: Quantum Detection and Estimation Theory. Academic Press, New York (1976)

    MATH  Google Scholar 

  2. Holevo, A.S.: Probabilistic and Statistical Aspects of Quantum Theory. North-Holland, Amsterdam (1982)

    MATH  Google Scholar 

  3. Hübner, M.: Explicit computation of the Bures distance for density matrices. Phys. Lett. A 163, 239 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  4. Hübner, M.: Computation of Uhlmann’s parallel transport for density matrices and the Bures metric on three-dimensional Hilbert space. Phys. Lett. A 179, 226 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  5. Braunstein, S.L., Caves, C.M.: Statistical Distance and the Geometry of Quantum States. Phys. Rev. Lett. 72, 3439 (1994)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Bollinger, J.J., Itano, W.M., Wineland, D.J., Heinzen, D.J.: Optimal frequency measurements with maximally correlated states. Phys. Rev. A 54, R4649 (1996)

    Article  ADS  Google Scholar 

  7. Bužek, V., Derka, R., Massar, S.: Optimal Quantum Clocks. Phys. Rev. Lett. 82, 2207 (1999)

    Article  ADS  Google Scholar 

  8. Peters, A., Chung, K.Y., Chu, S.: Measurement of gravitational acceleration by dropping atoms. Nature (London) 400, 849 (1999)

    Article  ADS  Google Scholar 

  9. Jozsa, R., Abrams, D.S., Dowling, J.P., Williams, C.P.: Quantum Clock Synchronization Based on Shared Prior Entanglement. Phys. Rev. Lett. 85, 2010 (2000)

    Article  ADS  Google Scholar 

  10. Tóth, G., Apellaniz, L.: Quantum metrology from a quantum information science perspective. J. Phys. A: Math. Theor. 47, 424006 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Yurke, B., McCall, S.L., Klauder, J.R.: SU(2) and SU(1, 1)interferometers. Phys. Rev. A 33, 4033 (1986)

    Article  ADS  Google Scholar 

  12. Dowling, J.P.: Correlated input-port, matter-wave interferometer: Quantum-noise limits to the atom-laser gyroscope. Phys. Rev. A 57, 4736 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  13. Kok, P., Braunstein, S.L., Dowling, J.P.: Quantum lithography, entanglement and Heisenberg-limited parameter estimation. J. Opt. B: Quantum Semiclassical Opt. 6, S811 (2004)

    Article  ADS  Google Scholar 

  14. Giovannetti, V., Lloyd, S., Maccone, L.: Quantum-enhanced measurements: Beating the standard quantum limit. Science 306, 1330 (2004)

    Article  ADS  Google Scholar 

  15. Giovannetti, V., Lloyd, S., Maccone, L.: Quantum Metrology. Phys. Rev. Lett. 96, 010401 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  16. Boixo, S., Flammia, S.T., Caves, C.M., Geremia, J.M.: Generalized Limits for Single-Parameter Quantum Estimation. Phys. Rev. Lett. 98, 090401 (2007)

    Article  ADS  Google Scholar 

  17. Roy, S.M., Braunstein, S.L.: Exponentially Enhanced Quantum Metrology. Phys. Rev. Lett. 100, 220501 (2008)

    Article  ADS  Google Scholar 

  18. Boixo, S., Datta, A., Davis, M.J., Flammia, S.T., Shaji, A., Caves, C.M.: Quantum Metrology: Dynamics versus Entanglement. Phys. Rev. Lett. 101, 040403 (2008)

    Article  ADS  Google Scholar 

  19. Hofmann, H.F.: All path-symmetric pure states achieve their maximal phase sensitivity in conventional two-path interferometry. Phys. Rev. A 79, 033822 (2009)

    Article  ADS  Google Scholar 

  20. Estève, J., Gross, C., Weller, A., Giovanazzi, S., Oberthaler, M.K.: Squeezing and entanglement in a Bose–Einstein condensate. Nature (London) 455, 1216 (2008)

    Article  ADS  Google Scholar 

  21. Hyllus, P., Pezzé, L., Smerzi, A.: Entanglement and Sensitivity in Precision Measurements with States of a Fluctuating Number of Particles. Phys. Rev. Lett. 105, 120501 (2010)

    Article  ADS  Google Scholar 

  22. Pezzé, L., Smerzi, A.: Entanglement, Nonlinear Dynamics, and the Heisenberg Limit. Phys. Rev. Lett. 102, 100401 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  23. Hyllus, L., Laskowski, W., Krischek, R., Schwemmer, C., Wieczorek, W., Weinfurter, H., Pezzé, L., Smerzi, A.: Fisher information and multiparticle entanglement. Phys. Rev. A 85, 022321 (2012)

    Article  ADS  Google Scholar 

  24. Tóth, G.: Multipartite entanglement and high precision metrology. Phys. Rev. A 85, 022322 (2012)

    Article  ADS  Google Scholar 

  25. Rosenkranz, M., Jaksch, D.: Parameter estimation with cluster states. Phys. Rev. A 79, 022103 (2009)

    Article  ADS  Google Scholar 

  26. Huelga, S.F., Macchiavello, C., Pellizzari, T., Ekert, A.K., Plenio, M.B., Cirac, J.I.: Improvement of Frequency Standards with Quantum Entanglement. Phys. Rev. Lett. 79, 3865 (1997)

    Article  ADS  Google Scholar 

  27. Ulam-Orgikh, D., Kitagawa, M.: Spin squeezing and decoherence limit in Ramsey spectroscopy. Phys. Rev. A 64, 052106 (2001)

    Article  ADS  Google Scholar 

  28. Sasaki, M., Ban, M., Barnett, S.M.: Optimal parameter estimation of a depolarizing channel. Phys. Rev. A 66, 022308 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  29. Shaji, A., Caves, C.M.: Qubit metrology and decoherence. Phys. Rev. A 76, 032111 (2007)

    Article  ADS  Google Scholar 

  30. Monras, A., Paris, M.G.A.: Optimal Quantum Estimation of Loss in Bosonic Channels. Phys. Rev. Lett. 98, 160401 (2007)

    Article  ADS  Google Scholar 

  31. Demkowicz-Dobrzański, R., Kołodyński, J., Guta, M.: The elusive Heisenberg limit in quantumenhanced metrology. Nat. Commun. 3, 1063 (2012)

    Article  Google Scholar 

  32. Demkowicz-Dobrzański, R., Dorner, U., Smith, B.J., Lundeen, J.S., Wasilewski, W., Banaszek, K., Walmsley, I.A.: Quantum phase estimation with lossy interferometers. Phys. Rev. A 80, 013825 (2009)

    Article  ADS  Google Scholar 

  33. Lee, T.-W., Huver, S.D., Lee, H., Kaplan, L., McCracken, S.B., Min, C., Uskov, D.B., Wildfeuer, C.F., Veronis, G., Dowling, J.P.: Optimization of quantum interferometric metrological sensors in the presence of photon loss. Phys. Rev. A 80, 063803 (2009)

    Article  ADS  Google Scholar 

  34. Dorner, U., Demkowicz-Dobrzański, R., Smith, B.J., Lundeen, J.S., Wasilewski, W., Banaszek, K., Walmsley, I.A.: Optimal Quantum Phase Estimation. Phys. Rev. Lett. 102, 040403 (2009)

    Article  ADS  Google Scholar 

  35. Watanabe, Y., Sagawa, T., Ueda, M.: Optimal Measurement on Noisy Quantum Systems. Phys. Rev. Lett. 104, 020401 (2010)

    Article  ADS  Google Scholar 

  36. Knysh, S., Smelyanskiy, V.N., Durkin, G.A.: Scaling laws for precision in quantum interferometry and the bifurcation landscape of the optimal state. Phys. Rev. A 83, 021804 (2011)

    Article  ADS  Google Scholar 

  37. Kołdyński, J., Demkowicz-Dobrzański, R.: Phase estimation withoutaprioriphase knowledge in the presence of loss. Phys. Rev. A 82, 053804 (2010)

    Article  ADS  Google Scholar 

  38. Kacprowicz, M., Demkowicz-Dobrzański, R., Wasilewski, W., Banaszek, K., Walmsley, I.A.: Experimental quantum-enhanced estimation of a lossy phase shift. Nat. Photonics 4, 357 (2010)

    Article  ADS  Google Scholar 

  39. Genoni, M.G.A., Olivares, S., Paris, M.G.: Optical Phase Estimation in the Presence of Phase Diffusion. Phys. Rev. Lett. 106, 153603 (2011)

    Article  ADS  Google Scholar 

  40. Chin, A.W., Huelga, S.F., Plenio, M.B.: Quantum Metrology in Non-Markovian Environments. Phys. Rev. Lett. 109, 233601 (2012)

    Article  ADS  Google Scholar 

  41. Escher, B.M., de MatosFilho, R.L., Davidovich, L.: General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology. Nat. Phys. 7, 406 (2011)

  42. Ma, J., Huang, Y., Wang, X., Sun, C.: Quantum Fisher information of the Greenberger-Horne-Zeilinger state in decoherence channels. Phys. Rev. A 84, 022302 (2011)

    Article  ADS  Google Scholar 

  43. Zhong, W., Sun, Z., Ma, J., Wang, X., Nori, F.: Fisher information under decoherence in Bloch representation. Phys. Rev. A 87, 022337 (2013)

    Article  ADS  Google Scholar 

  44. Chaves, R., Brask, J.B., Markiewicz, M., Kołodyński, J., Acín, A.: Noisy Metrology beyond the Standard Quantum Limit. Phys. Rev. Lett. 111, 120401 (2013)

    Article  ADS  Google Scholar 

  45. Jin, Y., Yu, H.: Electromagnetic shielding in quantum metrology. Phys. Rev. A 91, 022120 (2015)

    Article  ADS  Google Scholar 

  46. Jin, Y.: Precision protection through indirect correlations. Ann. Phys. (NY) 367, 212 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  47. Unruh, W.G.: Notes on black-hole evaporation. Phys. Rev. D 14, 870 (1976)

    Article  ADS  Google Scholar 

  48. Matsas, G.E.A., Vanzella, D.A.T.: Decay of protons and neutrons induced by acceleration. Phys. Rev. D 59, 094004 (1999)

    Article  ADS  Google Scholar 

  49. Vanzella, D.A.T., Matsas, G.E.A.: Decay of Accelerated Protons and the Existence of the Fulling-Davies-Unruh Effect. Phys. Rev. Lett. 87, 151301 (2001)

    Article  ADS  Google Scholar 

  50. Suzuki, H., Yamada, K.: Analytic evaluation of the decay rate for an accelerated proton. Phys. Rev. D 67, 065002 (2003)

    Article  ADS  Google Scholar 

  51. Higuchi, A., Matsas, G.E.A., Sudarsky, D.: Bremsstrahlung and Fulling-Davies-Unruh thermal bath. Phys. Rev. D 46, 3450 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  52. Higuchi, A., Matsas, G.E.A., Sudarsky, D.: Bremssstrahlung and zero-energy Rindler photons. Phys. Rev. D 45, 3308 (1992)

    Article  ADS  Google Scholar 

  53. Benatti, F., Floreanini, R.: Entanglement generation in uniformly accelerating atoms: Reexamination of the Unruh effect. Phys. Rev. A 70, 012112 (2004)

    Article  ADS  Google Scholar 

  54. Zhang, J., Yu, H.: Unruh effect and entanglement generation for accelerated atoms near a reflecting boundary. Phys. Rev. D 75, 104014 (2007)

    Article  ADS  Google Scholar 

  55. Audretsch, J., Müller, R.: Spontaneous excitation of an accelerated atom: The contributions of vacuum fluctuations and radiation reaction. Phys. Rev. A 50, 1755 (1994)

    Article  ADS  Google Scholar 

  56. Audretsch, J., Müller, R.: Radiative energy shifts of an accelerated two-level system. Phys. Rev. A 52, 629 (1995)

    Article  ADS  Google Scholar 

  57. Audretsch, J., Müller, R., Holzmann, M.: Generalized Unruh effect and Lamb shift for atoms on arbitrary stationary trajectories. Class. Quant. Grav. 12, 2927 (1995)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  58. Passante, R.: Radiative level shifts of an accelerated hydrogen atom and the Unruh effect in quantum electrodynamics. Phys. Rev. A 57, 1590 (1997)

    Article  ADS  Google Scholar 

  59. Zhu, Z., Yu, H., Lu, S.: Spontaneous excitation of an accelerated hydrogen atom coupled with electromagnetic vacuum fluctuations. Phys. Rev. D 73, 107501 (2006)

    Article  ADS  Google Scholar 

  60. Zhou, W., Yu, H.: Spontaneous excitation of a uniformly accelerated atom coupled to vacuum Dirac field fluctuations. Phys. Rev. A 86, 033841 (2012)

    Article  ADS  Google Scholar 

  61. Li, Q., Yu, H., Zhou, W.: Response of a uniformly accelerated detector to massless Rarita–Schwinger fields in vacuum . Ann. Phys. (NY) 348, 144 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  62. Hu, J., Yu, H.: Geometric phase for an accelerated two-level atom and the Unruh effect. Phys. Rev. A 85, 032105 (2012)

    Article  ADS  Google Scholar 

  63. Gorini, V., Kossakowski, A., Surdarshan, E.C.G.: Completely positive dynamical semigroups of N-level systems. J. Math. Phys. 17, 821 (1976)

    Article  ADS  MathSciNet  Google Scholar 

  64. Gorini, V., Kossakowski, A., Surdarshan, E.C.G., Lindblad, G.: On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976)

    Article  MathSciNet  Google Scholar 

  65. Benatti, F., Floreanini, R., Piani, M.: Environment Induced Entanglement in Markovian Dissipative Dynamics. Phys. Rev. Lett. 91, 070402 (2003)

    Article  ADS  Google Scholar 

  66. Greiner, W., Reinhardt, J.: Field Quantization. Springer (1996)

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Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grants No. 11605030, and the Scientific Research Foundation of Guiyang university under Grant No. 20160375115.

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  1. School of Electronic and Communication Engineering, Guiyang University, Guiyang, Guizhou, 550005, China

    Yao Jin

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Jin, Y. The Effect of Vacuum Fluctuations on Quantum Metrology for a Uniformly Accelerated Atom. Int J Theor Phys 56, 898–905 (2017). https://doi.org/10.1007/s10773-016-3232-3

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